It appears that the Postgres "server-prepared statement" cannot handle parameters to the statement. This is really unfortunate, because 99% of real-life applications will want to re-use the same statement (template) with different parameters.
The term "server-prepared statement" itself already indicates that there may be something skewed about the "local" semantics of java.sql.PreparedStatements in the Postgres JDBC driver. There is no notion of "client-prepared statement" in the JDBC API, which conceives PreparedStatement instances as mere handles to server side objects. And indeed, Postgres JDBC users have historically been using java.sql.PreparedStatements for its side-effect of preventing SQL injection rather than for the purpose the JDBC API designers had in mind with this class.
I'm not sure where this hypothesis is coming from. Postgresql server prepared statements can certainly handle parameters.
